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Fano varieties with $$\hbox {Nef}(X)$$Nef(X) = $$\hbox {Psef}(X)$$Psef(X) and $$\rho (X)$$ρ(X) = $$\hbox {dim}\,X-1$$dimX-1

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0 Published in 2018 at "manuscripta mathematica"

DOI: 10.1007/s00229-018-1015-2

Abstract: We classify mildly singular Fano varieties X such that $$\mathrm {Nef}(X)=\mathrm {Psef}(X)$$Nef(X)=Psef(X) and $$\rho (X)=\mathrm {dim}\,X-1$$ρ(X)=dimX-1. read more here.

Keywords: dim dimx; fano varieties; psef; hbox ... See more keywords

Toric Fano varieties associated to graph cubeahedra

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1 Published in 2018 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1933997

Abstract: Abstract We give a necessary and sufficient condition for the nonsingular projective toric variety associated to the graph cubeahedron of a finite simple graph to be Fano or weak Fano in terms of the graph. read more here.

Keywords: graph cubeahedra; fano; fano varieties; associated graph ... See more keywords

On the Chow ring of Fano varieties on the Fatighenti–Mongardi list

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2 Published in 2021 at "Communications in Algebra"

DOI: 10.1080/00927872.2021.1955900

Abstract: Conjecturally, Fano varieties of K3 type admit a multiplicative Chow–Künneth decomposition, in the sense of Shen–Vial. We prove this for many of the families of Fano varieties of K3 type constructed by Fatighenti–Mongardi. This has… read more here.

Keywords: fano varieties; chow ring; varieties fatighenti; fatighenti mongardi ... See more keywords

The volume of singular Kähler–Einstein Fano varieties

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1 Published in 2018 at "Compositio Mathematica"

DOI: 10.1112/s0010437x18007042

Abstract: We show that the anti-canonical volume of an $n$ -dimensional Kähler–Einstein $\mathbb{Q}$ -Fano variety is bounded from above by certain invariants of the local singularities, namely $\operatorname{lct}^{n}\cdot \operatorname{mult}$ for ideals and the normalized volume function… read more here.

Keywords: einstein fano; hler einstein; fano varieties; volume ... See more keywords